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Signal Detection for Ultra-Massive MIMO: An Information Geometry Approach

Jiyuan Yang, Yan Chen, Xiqi Gao, Dirk Slock, Xiang-Gen Xia

TL;DR

This work tackles the challenging problem of signal detection in ultra-massive MIMO, where MAP/ML detectors are NP-hard. It introduces an information geometry-based SD (IGA-SD) that recasts posterior marginals as an exponential-family problem and computes them via iterative m-projections between an independent objective manifold and interacting auxiliary manifolds, using Lyapunov CLT to obtain tractable Gaussian approximations. The resulting MPM detector relies on approximate a posteriori marginals p_k(s_k|y) with updates guided by the natural parameters on an embedded e-flat manifold, achieving a per-iteration complexity of $O(16 N_r K (L+1))$ and competitive BER performance. Simulations across 4-, 16-, and 64-QAM demonstrate that IGA-SD can outperform LMMSE, AMP, and EP with fewer iterations, indicating strong potential for scalable, efficient detection in future ultra-massive MIMO systems.

Abstract

In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.

Signal Detection for Ultra-Massive MIMO: An Information Geometry Approach

TL;DR

This work tackles the challenging problem of signal detection in ultra-massive MIMO, where MAP/ML detectors are NP-hard. It introduces an information geometry-based SD (IGA-SD) that recasts posterior marginals as an exponential-family problem and computes them via iterative m-projections between an independent objective manifold and interacting auxiliary manifolds, using Lyapunov CLT to obtain tractable Gaussian approximations. The resulting MPM detector relies on approximate a posteriori marginals p_k(s_k|y) with updates guided by the natural parameters on an embedded e-flat manifold, achieving a per-iteration complexity of and competitive BER performance. Simulations across 4-, 16-, and 64-QAM demonstrate that IGA-SD can outperform LMMSE, AMP, and EP with fewer iterations, indicating strong potential for scalable, efficient detection in future ultra-massive MIMO systems.

Abstract

In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.
Paper Structure (11 sections, 4 theorems, 125 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 4 theorems, 125 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. System Configuration
  4. Problem Statement
  5. Preliminaries of Information Geometry
  6. Information Geometry Approach for Signal Detection
  7. Simulation Results
  8. Conclusion
  9. Proof of Theorem \ref{['lemma:equivalent of mp1']}
  10. Proof of Corollary \ref{['the:equivalent of mp2']}
  11. Proof of Theorem \ref{['the:CLT of Y_n,k']}

Key Result

Theorem 1

Given $p\left( \mathbf{s} \right) \in \mathcal{S}$, and the $e$-flat $\mathcal{M}_0 \subseteq \mathcal{S}$, the $m$-projection of $p\left( \mathbf{s} \right)$ onto $\mathcal{M}_0$ is unique. Moreover, $p_0\left(\mathbf{s};{\boldsymbol\theta}_{0}^{\star}\right)$ is the $m$-projection of $p\left( \mat where ${\boldsymbol\eta}, {\boldsymbol\eta}_0\left({\boldsymbol\theta}_{0}^{\star}\right) \in \math

Figures (6)

  • Figure 1: BER performance of IGA compared with AMP, EP and LMMSE under $4$-QAM.
  • Figure 2: Convergence performance of IGA compared with EP and AMP at SNR = $5$ dB under $4$-QAM.
  • Figure 3: BER performance of IGA compared with AMP, EP and LMMSE under $16$-QAM.
  • Figure 4: BER performance of IGA compared with AMP, EP and LMMSE under $64$-QAM.
  • Figure 5: Convergence performance of IGA compared with EP and AMP at SNR = $14$ dB under $16$-QAM.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Lemma 1: Lyapunov central-limit-theorem billingsley2008probability
  • Theorem 2
  • proof